Many cryptographic protocols employ operations wherein a point on an elliptic curve is multiplied by large scalar values. In order to cut down on such computationally demanding operations, double and add algorithms are frequently employed to multiply the point by the scalar. In a further development, a non-adjacent digit set (NADS) can be used to optimize arithmetic operations performed on elliptic curves in cryptographic applications. For example, the set {−1, 0, 1} provides options not seen in the conventional binary number system whose digits are {0, 1}.
Recently, use of digit sets having the format {0, 1, x} where x is a negative integer has been explored. This technology has resulted in increased computational efficiency of calculations involving multiplication of large integers and elliptic curve points. Unfortunately, while computational efficiencies have increased, such algorithms continue to be subject to side-channel attacks. The existing literature typically involves very small values of x, which limit the amount of randomness that can be entered into the computation.